This type of modelling method is known for example from DE-A-101 29 565. In this publication in particular an attempt was made for the first time to resolve the Fourier thermal conductivity equation itself and not to resolve an incorrect variation of this thermal conductivity equation, in order to correctly describe the thermodynamic behavior of a steel band. This publication is thus included by reference it in the disclosed content of the present invention.
Such a modelling method is also described in the older German Patent Application 102 51 716.9 not published at the time of the present application. With this modelling method an attempt is made to model the phase conversion of the steel on the basis of the Gibbs free enthalpies of the steel. This publication too is thus included by reference to it in the disclosed content of the present invention.
This type of modelling method is also known from the paper “Numerische Simulation der Wärmeleitung in Stahlblechen—Mathematik hilft bei der Steuerung von Kühlstrecken” (numerical simulation of thermal conductivity in steel sheets—mathematics helps in the control of cooling lines) by W. Borchers et al., published in the University periodical of the Friedrich-Alexander University Erlangen-Nürnberg, Volume 102, Oct. 27, 2001 year.
Finally traditional approaches in accordance with the Scheilen rule, according to Johnson-Mehl-Avrami and Brimacombe, are known.
The exact modelling of the temperature curve of steel over time during cooling down, especially of steel bands, is decisive for the control of the required water or coolant amounts of a cooling line for steel. This is because the transformation of the steel which occurs during cooling down decisively influences the thermal behavior of the steel as it cools down. Major material properties of the steel are also influenced by the cooling down process. Since the cooling down does not occur in thermal equilibrium however, it is not possible to describe the transformation simply by suitable adaptation of the thermal capacity. Thus an exact modelling of the phase change of the steel is also required in order to enable the cooling line to be controlled correctly.
In practice the traditional approaches of the prior art do not operate without errors in all cases. In particular they exhibit a series of systematic disadvantages. First of all separate parameters must be set for each material. Interpolations between different materials are not possible or at least only possible to a restricted extent. Secondly only two phases are considered in the traditional method of the prior art. An expansion to more than two phases is not possible for system reasons. Thirdly the traditional prior art methods only deliver a good match between model and reality for a complete change of the metal observed. Fourthly the traditional prior art methods do not provided any information about the heat released during the phase change. The knowledge of the phase change heat is however an absolute necessity for a correct solution of the thermal conduction equation.
The methodologies according to DE-A-101 29 565 and the technical paper “Numerische Simulation . . . ” already represent a significant advance by comparison with such methods, since they at least describe the thermal conduction completely correctly. The older German Patent Application additionally improves the modelling of the phase change. In particular it supplies the change heat which occurs during the phase change. However these methods are also not capable of improvement.